Question

Which ordered pair is a solution to the system of equations? {(y=3x),(y=2x+3)} (3,9) (2,6) (2,7) (1,3)

Answer 1

To find the solution to the given system of equations, we need to substitute the values of x and y into each equation and check if they satisfy the equations. (3,9) is the only ordered pair that satisfies both equations.

Step-by-step explanation:

To determine which ordered pair is a solution to the system of equations, we need to substitute the values of x and y into each equation and check if the equations are satisfied. Let's check each option:

1. For the ordered pair (3,9), in the first equation, y = 3(3) = 9, which is true. In the second equation, y = 2(3) + 3 = 9, which is also true. Therefore, (3,9) is a solution to the system of equations.
2. For the ordered pair (2,6), in the first equation, y = 3(2) = 6, which is true. In the second equation, y = 2(2) + 3 = 7, which is not true. Therefore, (2,6) is not a solution to the system of equations.
3. For the ordered pair (2,7), in the first equation, y = 3(2) = 6, which is not true. In the second equation, y = 2(2) + 3 = 7, which is true. Therefore, (2,7) is not a solution to the system of equations.
4. For the ordered pair (1,3), in the first equation, y = 3(1) = 3, which is true. In the second equation, y = 2(1) + 3 = 5, which is not true. Therefore, (1,3) is not a solution to the system of equations.

Based on the above analysis, the ordered pair (3,9) is the only solution to the system of equations.